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Proof step 8 from proof app (previous step)

unique_al((p0 ' + ax0) + p ' + ay), ∀ p, ay. unique_al(ax0 + p ' + ay) → ax0 + ay = [] ∨ ¬ (ax0 + ay).head.1 ∈ (ax0 + ay).tail ∧ unique_al((ax0 + ay).tail) ⊦ ¬ p0.1 ∈ ax0 ∧ ¬ p0.1 ∈ ay ∧ unique_al(ax0 + ay)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ unique_al(ay) ↔ ay = [] ∨ ¬ ay.head.1 ∈ ay.tail ∧ unique_al(ay.tail)
Proof step 10:
∀ p, ay. unique_al(ax0 + p ' + ay) → ax0 + ay = [] ∨ ¬ (ax0 + ay).head.1 ∈ (ax0 + ay).tail ∧ unique_al((ax0 + ay).tail), (p0 ' + ax0) + p ' + ay = [] ∨ ¬ ((p0 ' + ax0) + p ' + ay).head.1 ∈ ((p0 ' + ax0) + p ' + ay).tail ∧ unique_al(((p0 ' + ax0) + p ' + ay).tail) ⊦ ¬ p0.1 ∈ ax0 ∧ ¬ p0.1 ∈ ay ∧ unique_al(ax0 + ay)

Rule argument

spec: <toplevel> name: k-unique-r seq: ⊦ unique_al(ay) ↔ ay = [] ∨ ¬ ay.head.1 ∈ ay.tail ∧ unique_al(ay.tail) subst: [ay] → [(p0 ' + ax0) + p ' + ay] flags: <all paths>

Additional information

Used terms: (p0 ' + ax0) + p ' + ay